Differences In Marginal Costs Research Articles

Information transmit strategy of e-commerce platform with financially constrained supplier

A signaling game model is constructed in the framework of a supply chain system consisting of a financially constrained supplier and an e-commerce platform acting as marketplace and a creditor simultaneously. The primary concern of this work is to investigate how the e-commerce platform, which has superior information about market demand, indirectly communicates this information to the financially constrained supplier through its marketing efforts. Under both separating and pooling equilibria, the decisions and profits of each member of the supply chain are firstly considered. Furthermore, using an “intuitive criterion”, the e-commerce platform’s dominant strategy and its influencing factors are analyzed. The results show that when there is a significant difference in the marginal marketing costs, the platform tends to choose the separating equilibrium. When the difference in marginal marketing costs is relatively slight, the e-commerce platform’s dominant strategy depends on the capital of the supplier and the level of market demand fluctuations. Specifically, the e-commerce platform will select the pooling equilibrium when market demand fluctuations are minimal, but the platform will select the separating equilibrium when market demand fluctuations are substantially large. If the supplier’s capital is increased within a certain range, the e-commerce platform is more motivated to select the pooling equilibrium. In addition, the platform usage fee ratio, the platform loan interest rate and the supplier’s prior beliefs are important factors influencing the platform’s decision.

The impact of brand equity on profit premium in an equilibrium framework

AbstractRecent research extends the estimation and analysis of structural demand and supply models to consider the concepts of brand equity and brand value and their role in product investment decisions. In this paper, we analyze data from the Dutch market for new cars to show that differences in brand equity may also entail significant differences in marginal costs. Next, we illustrate that ignoring the role of brand equity in marginal costs, as the existing literature has, ignores the possibility that investments in brand equity may actually reduce the marginal profits for the offering. This can change investment incentives and produce different market structures.

Co-benefits and influencing factors exploration of air pollution and carbon reduction in China: Based on marginal abatement costs

This study addresses the pressing need for cost-effective emission reduction strategies that maximize co-benefits in terms of air pollution and carbon emissions. Our research contributes to the literature by accurately measuring these co-benefits, thereby facilitating their prompt realization in different regions. We employ an input-output framework that integrates carbon emissions and air pollution, allowing us to calculate marginal abatement costs using the shadow price of undesired output. Through this approach, we quantify the co-benefits and analyze the factors influencing them at both spatiotemporal and factor levels using spatial kernel density and geographical detectors. Our findings reveal several key insights: (1) under joint emission reduction efforts, we observe average annual reduction rates of 6.46% for marginal pollution and 6.10% for carbon reduction costs. Importantly, we document an increase in co-benefits from 0.50 to 0.86, characterized by an initial fluctuation followed by a linear increase. (2) the marginal cost difference for carbon emission and pollution reduction in western China was 179.45 and 155.08 respectively, compared to 321.51 and 124.70 in the Northeast, highlighting the crucial role of regional differences in shaping co-benefit outcomes. (3) we identify a negative spatial spillover effect between provinces, which diminishes over time, leading to heterogeneous effects when local provincial co-benefits exceed a threshold of 0.9. (4) during the adjustment period, we find that the industrial structure exerts significant single and interactive effects on co-benefits. Additionally, we highlight the critical role of environmental governance investment and government intervention as drivers of co-benefits in the current era. By offering the quantification of co-benefits under the marginal abatement costs, our study provides valuable scientific insights for planning and implementing effective synergy strategies.

Energy storage as a service to achieve a required reliability level for renewable-rich standalone microgrids

Energy storage systems (ESSs) can help to reduce the intermittency and uncertainty of renewable energy supplies in power systems. ESSs are critical components of renewable-rich standalone microgrids (SMGs) to balance power generation and load demand, which is referred to as reliability. To achieve the same level of reliability as conventional power systems for renewable-based SMGs, significant investment in ESSs is required. However, due to the high investment costs of ESSs, the installation of large ESSs will not result in an affordable solution for achieving renewable SMG at the required reliability. As a result, this paper proposes a new sharing concept for ESS, namely energy storage as a service (ESaaS), to be implemented across microgrids as a low-cost alternative for improving reliability. In the proposed ESaaS concept, microgrids can use ESS from an ESS provider as required for different timeframes such as monthly, weekly, or daily, depending on the renewable resources and load profile characteristics. In this paper, the use of ESaaS is investigated over a range of timeframes for a 100 % renewable-based SMG with photovoltaic (PV), wind turbine (WT), and ESS. The SMG reliability is evaluated using Monte Carlo simulation both before and after the ESaaS strategy has been implemented. To evaluate the ESaaS affordability in improving the reliability of an SMG, this paper proposes the criteria of marginal cost of reliability, which indicates the rate of additional investment amount per percentage of reliability improvement. The marginal cost of reliability combines the economic and technical aspects of ESaaS in one simple criterion for effective decision-making among investment strategies such as different timeframes of ESaaS or permanent ESS. The simulation results show the ESaaS based on daily contract results in a lower marginal cost of reliability for the case study. To validate the effectiveness of the proposed ESaaS approach using marginal cost of reliability, the levelized cost of electricity (LCOE) is also calculated for different strategies of reliability improvement. The results confirm that the lowest LCOE is obtained using the strategy that provides the lowest marginal cost of reliability for the case study. In addition, a sensitivity analysis is performed to assess the difference in marginal cost of reliability under various uncertainties associated with the installed capacity of PV and WT, and the cost of utilising the ESaaS.

A cost comparison of benralizumab, mepolizumab, and dupilumab in patients with severe asthma: A US third-party payer perspective.

BACKGROUND: Clinical trials and real-world evidence (RWE) studies of biologics have demonstrated reduced exacerbations, decreased use of oral corticosteroids (OCS), and improvements in daily symptoms and health-related quality of life in patients with severe eosinophilic asthma (SEA). OBJECTIVE: To compare direct health care costs associated with biologic use for the treatment of SEA from a US third-party payer perspective. METHODS: We developed a cost-minimization model to compare costs and cost offsets associated with 3 biologics-benralizumab, mepolizumab, and dupilumab-for 2- and 4-year periods. The model relied on longitudinal data from clinical trials to inform the primary (base case) analysis cost comparison and RWE study data, in a separate scenario, to compare costs in nonclinical trial settings. Primary model outcomes included exacerbations (including hospitalizations), OCS-dependent years (including associated complications), and total direct health care biologic costs. Results were calculated at the per patient and population level (per 1,000 patients). Sensitivity analyses with key model parameters were performed. RESULTS: Benralizumab had the lowest total biologic costs per patient for both the 2- and 4-year periods. Over 4 years, the marginal cost difference in total biologic costs per patient was $23,061 lower for benralizumab vs mepolizumab and $17,242 lower for benralizumab vs dupilumab. The 4-year population level analysis of benralizumab vs mepolizumab revealed $4.8 million in marginal cost offsets due to 582 fewer exacerbations and 153 fewer OCS-dependent years and a marginal total cost savings of $27.9 million per 1,000 patients for benralizumab. The 4-year population level analysis of benralizumab vs dupilumab revealed $2.3 million in marginal cost offsets due to 291 fewer exacerbations and 64 fewer OCS-dependent years and marginal total cost savings of $19.5 million per 1,000 patients for benralizumab. RWE data were available for a 2-year cost comparison scenario of benralizumab vs mepolizumab, which showed similar results to the base case analysis. Sensitivity analyses varying assumptions on key model parameter estimates confirmed results, with benralizumab having lower total direct health care costs in all scenarios tested, and showed that model results were most sensitive to changes in biologic costs and exacerbation reduction rates. CONCLUSIONS: Patients receiving benralizumab had higher nonbiologic cost offsets because of reductions in exacerbations and OCS-dependent years, leading to greater cost savings for third-party payers compared with patients receiving mepolizumab or dupilumab. Taken together with biologic costs, benralizumab presents greater savings in health care costs for payers than patients with SEA who use mepolizumab or dupilumab. DISCLOSURES: This study was funded by AstraZeneca (Cambridge, UK). Drs Xu, Chung, Genofre, and Katial are or were AstraZeneca employees at the time this research was conducted and may be shareholders of AstraZeneca. Ms Schaefer and Dr Szende are employees of Labcorp Drug Development, which received funding from AstraZeneca to perform this research.

The Economic Burden of Multiple Myeloma. Definition of a Model for Forecasting Patients’ Costs


 Background: The aim of this study was to evaluate healthcare costs in a single-centre population of patients with multiple myeloma (MM), in an attempt to develop a model for forecasting costs.
 Methods: A cohort of 387 MM patients, diagnosed at Policlinico San Matteo (Pavia, Italy), between 2002 and 2014, was analysed grouping patients into those eligible (n=223) or not eligible (n=164) for transplantation. After descriptive statistics, the benchmark model - Ordinary Least Squares - and different variations of the Generalized Linear Model were adopted.
 Results: The average total cost per patient was around €28,500 for patients not eligible for transplantation and around €87,000 for the eligible ones. The difference in marginal costs for transplant-eligible patients was probably due to higher costs for hospitalisation and the costs of the transplant procedure itself. The analysis highlighted four determinants useful for building a model to forecast expenditure: age, bortezomib use, lenalidomide use, and number of lines of therapies. The two most important determinants of expenditure were use of the novel agents and the total number of lines of therapy, which reflects a higher number of doses and a greater need for accesses to hospital.
 Conclusion: In conclusion, using a Generalized Linear Model, we identified four determinants in our cohort which were useful for building a model to predict expenditure for MM patients. Although the analysis was performed in a particular setting in a single hospital, the model could be applied to any scenario of patients.

Third‐Degree Price Discrimination in Oligopoly when Markets are Covered*

We analyze oligopolistic third‐degree price discrimination relative to uniform pricing when markets are covered. Pricing equilibria are critically determined by supply‐side features such as the number of firms and their marginal cost differences. It follows that each firm's Lerner index under uniform pricing is equal to the weighted harmonic mean of the firm's relative margins under discriminatory pricing. Uniform pricing then lowers average prices and raises consumer surplus. We can calculate the gain in consumer surplus and loss in firms' profits from uniform pricing based only on the market data of the discriminatory equilibrium (i.e., prices and quantities).

Determining the Marginal Cost Differences of a Telehealth Versus an In-person Occupational Therapy Evaluation Session for Stroke Survivors Using Time-driven Activity-based Costing

ObjectiveTo estimate the marginal cost differences and care delivery process of a telerehabilitation vs outpatient session. DesignThis study used a time-driven activity-based costing approach including (1) observation of rehabilitation sessions and creation of manual time stamps, (2) structured and recorded interviews with 2 occupational therapists familiar with outpatient therapy and 2 therapists familiar with telerehabilitation, (3) collection of standard wages for providers, and (4) the creation of an iterative flowchart of both an outpatient and telerehabilitation session care delivery process. SettingTelerehabilitation and outpatient therapy evaluation. ParticipantsThree therapists familiar with care deliver for telerehabilitation or outpatient therapy (N=3). InterventionsNot applicable. Main Outcome MeasuresMarginal cost difference between telerehabilitation and outpatient therapy evaluations. ResultsOverall, telerehabilitation ($225.41) was more costly than outpatient therapy ($168.29) per session for a cost difference of $57.12. Primary time drivers of this finding were initial phone calls (0 minutes for OP therapists vs 35 minutes for TR) and post documentation (5 minutes for OP vs 30 minutes for TR) demands for telerehabilitation. ConclusionsTelerehabilitation is an emerging platform with the potential to reduce costs, improve health care inequities, and facilitate better patient outcomes. Improvements in documentation practices, staffing, technology, and reimbursement structuring would allow for a more successful translation.

Conflict and Corporate Social Responsibility in Duopoly

Abstract Background: Recent scientific research explains corporate social responsibility as an economic activity. This paper interprets social responsibility as a means of power to increase firms’ market share in a duopoly. Objectives: This paper analyses the duopoly model in which firms decide on optimal social investments and production in two phases. The basic research question is how the significance of the conflict affects social investments, market shares, production quantities, profits, and social welfare. Methods / Approach: Conflict technology is described by contest success functions determining market shares. Game theory, optimization, and comparative statics are used in the analysis. Results: The conditions of equilibrium existence and its characteristics are described. Conflict adversely affects the profit of the inefficient firm while it favourably affects social welfare. Conflict’s impact on an efficient firm’s profit depends on the marginal cost difference. Conclusions: If there is no significant cost difference, it is more favourable for firms not to invest in socially responsible activities by agreement, which hurts social welfare. When marginal cost difference is significant, corporate social responsibility increases an efficient firm’s profit, positively impacting social welfare.

Quantum Cournot duopoly game with general isoelastic demand and asymmetric production costs

This letter explores the quantum version of a Cournot duopoly game with general isoelastic demand and asymmetric production costs by applying Li-Du-Massar's minimal quantization rules, and it especially analyzes the existence region of quantum equilibrium, and the influences of quantum entanglement , difference in marginal costs (k) and elasticity of demand on the optimal profits of both firms. The results show that the existence region decreases with γ and k increasing. A larger elasticity of demand can destroy the profits of both firms. If positive γ and k are more favourable to the profits of two firms. If the first firm's profit increases with γ increasing for fixed k, but decreases with k increasing for fixed γ. The second firm's profit increases with k increasing for any fixed γ. As to the influences of γ on the second firm's profit, when k is less than a critical value, it increases with γ increasing, otherwise it decreases with γ increasing for fixed k.

507 a. Determining the marginal cost differences and potential areas of improvement for a telerehabilitation versus outpatient occupational therapy session for stroke survivors

OBJECTIVES/GOALS: The objective of this study was to estimate the cost differences of a telerehabilitation versus outpatient session. A secondary objective was to identify areas to improve telerehabilitation delivery efficiency. We aim to improve the translation/adoption of telerehabilitation for clinical use. METHODS/STUDY POPULATION: This study used a time-driven activity-based costing (TDABC) approach including 1) observation of rehabilitation sessions and creation of manual time stamps, 2) structured and recorded interviews with two occupational therapists familiar with outpatient therapy and two therapists familiar with telerehabilitation, 3) collection of standard wages for providers, and 4) the creation of an iterative flowchart of both an outpatient and telerehabilitation session care delivery process. This study followed the reporting guidelines to ensure a standardization for TDABC research. RESULTS/ANTICIPATED RESULTS: Overall, telerehabilitation ($225.41) was more costly than outpatient therapy ($168.29) per session for a cost difference of $57.12. Primary time drivers of this finding were initial phone calls (0 mins for OP therapists versus 35 mins for TR) and post documentation (5 mins for OP versus 30 mins for TR) demands for telerehabilitation. DISCUSSION/SIGNIFICANCE: Telerehabilitation is an emerging platform with the potential to reduce costs, improve healthcare inequities, and facilitate better patient outcomes. Improvements in documentation practices, staffing, technology, and reimbursement structuring would allow for a more successful translation.

Cost Optimized Building Energy Retrofit Measures and Primary Energy Savings under Different Retrofitting Materials, Economic Scenarios, and Energy Supply

We analyze conventional retrofit building materials, aluminum, rock, and glass wool materials and compared such materials with wood-based materials to understand the lifecycle primary energy implications of moving from non-renewable to wood-based materials. We calculate cost optimum retrofit measures for a multi-apartment building in a lifecycle perspective, and lifecycle primary energy savings of each optimized measure. The retrofit measures consist of the thermal improvement of windows with varied frame materials, as well as extra insulation of attic floor, basement walls, and external walls with varied insulation materials. The most renewable-based heat supply is from a bioenergy-based district heating (DH) system. We use the marginal cost difference method to calculate cost-optimized retrofit measures. The net present value of energy cost savings of each measure with a varied energy performance is calculated and then compared with the calculated retrofit cost to identify the cost optimum of each measure. In a sensitivity analysis, we analyze the cost optimum retrofit measures under different economic and DH supply scenarios. The retrofit costs and primary energy savings vary somewhat between non-renewable and wood-based retrofit measures but do not influence the cost optimum levels significantly, as the economic parameters do. The lifecycle primary use of wood fiber insulation is about 76% and 80% less than for glass wool and rock wool, respectively. A small-scale DH system gives higher primary energy and cost savings compared to larger DH systems. The optimum final energy savings, in one of the economic scenarios, are close to meeting the requirements in one of the Swedish passive house standards.

Iteration-Based Linearized Distribution-Level Locational Marginal Price for Three-Phase Unbalanced Distribution Systems

Distributed energy resources (DERs) are rocking the utilities’ business landscape. It calls for competitive market environments that incentivize DERs to form maximum operating efficiency. Among proposed pricing schemes, distribution-level locational marginal price (DLMP) is effective in signaling the marginal generation cost differences driven by energy losses and network constraints. It can be derived from a distribution-level optimal power flow (OPF) framework, as it essentially presents the sensitivity of optimized generation cost towards incremental loads. However, due to the high resistance-to-inductance ratio and unbalanced characteristics of distribution networks, computational affordable DLMPs are highly challenged. This article provides a linear-approximated DLMP that can be solved efficiently and generalized to account for reactive power flow, three-phase unbalanced loads and meshed network structure. The successive linear programming technique is introduced to enhance the model accuracy. Case studies on an IEEE 123-Bus system validate its accuracy against a nonlinear benchmark and capability in offering proper incentives.

Scaling up Climate Mitigation Policy in Germany

Germany has set national greenhouse emissions targets of a 65 percent reduction below 1990 levels by 2030 and net zero emissions by 2045, along with various sectoral emissions goals. To achieve these targets, the government has introduced multi-pronged policy measures, including a national emissions trading system (ETS), which complements the ETS at the EU level. This paper shows the substantial variation in the price responsiveness of emissions across sectors and thus prices implied by sectoral targets. It proposes the following measures to help Germany meet emissions targets with greater certainty and cost effectiveness: (i) further strengthening carbon pricing, for example through automatically rising price floors for the national ETS after 2026; (ii) harmonizing carbon pricing to reduce cross-sector differences in marginal abatement costs; and (iii) introducing feebates (revenue neutral taxsubsidy schemes) to reinforce incentives at the sectoral level. The paper also studies the distributional impact of higher carbon pricing and suggests that reducing social security contributions can mitigate the regressive direct impact of higher carbon pricing on lowerincome households. Concerns with carbon leakages and firms’ competitiveness are best addressed through agreeing on an international carbon price floor.

ELECTRICITY PRICE FUNDAMENTALS IN HYDROTHERMAL POWER GENERATION MARKETS USING MACHINE LEARNING AND QUANTILE REGRESSION ANALYSIS

A hydrothermal power generation market is characterized by a strong dependence on water reservoir capacity and fossil fuel sources, which causes differences in generation marginal costs and high variability of the electricity spot price. Therefore, this study proposes an empirical approach to identify the price determinants and their effects on price dynamics. This paper presents two methodologies: a machine learning approach and a quantile regression analysis. The first method is used to validate the price determinants through a prediction process, and the second, the quantile regression, to identify the non-linear effects. The most important factors observed are total market demand, water reservoirs capacity for generation, and fossil fuel consumption. The results offer a new perspective about the market structure and spot price volatility.Keywords: electricity prices; hydrothermal power generation markets; machine learning; quantile regression; Gaussian process regression.JEL Classifications: C22, Q41, Q43, Q47DOI: https://doi.org/10.32479/ijeep.11346

Do remote dialysis services really cost more? An economic analysis of hospital and dialysis modality costs associated with dialysis services in urban, rural and remote settings

BackgroundRates of end-stage kidney disease in Australia are highest in the Northern Territory (NT), with the burden of disease heaviest in remote areas. However, the high cost of delivering dialysis services in remote areas has resulted in centralisation, requiring many people to relocate for treatment. Patients argue that treatment closer to home improves health outcomes and reduces downstream healthcare use. Existing dialysis cost studies have not compared total health care costs associated with treatment in different locations.ObjectiveTo estimate and compare, from a payer perspective, the observed health service costs (all cause hospital admissions, emergency department presentations and maintenance dialysis) associated with different dialysis models in urban, rural and remote locations.MethodsUsing cost weights attributed to diagnostic codes in the NT Department of Health’s hospital admission data set (2008–2014), we calculated the mean (SD) total annual health service costs by dialysis model for 995 dialysis patients. Generalized linear modeling with bootstrapping tested the marginal cost differences between different explanatory variables to estimate ‘best casemix’/‘worst casemix’ cost scenarios.ResultsThe mean annual patient hospital expenditure was highest for urban models at $97 928 (SD $21 261) and $43 440 (SD $5 048) and lowest for remote at $19 584 (SD $4 394). When combined with the observed maintenance dialysis costs, expenditure was the highest for urban models at $148 510 (SD $19 774). The incremental cost increase of dialysing in an urban area, compared with a rural area, for a relocated person from a remote area, was $5 648 more and increased further for those from remote and very remote areas to $10 785 and $15 118 respectively.ConclusionsThis study demonstrates that dialysis treatment in urban areas for relocated people has health and cost implications that maybe greater than the cost of remote service delivery. The study emphasises the importance of considering all health service costs and cost consequences of service delivery models.Key points for decision makersRelocation for dialysis treatment has serious health and economic consequences. Relocated people have low dialysis attendance and high hospital costs in urban areas. While remote dialysis service models are more expensive than urban models, the comparative cost differences are significantly reduced when all health service costs are included. The delivery of equitable and accessible dialysis service models requires a holistic approach that incorporates the needs of the patient; hence dialysis cost studies must consider the full range of cost impacts beyond the dialysis treatments alone.

Cold versus hot endoscopic mucosal resection for large sessile colon polyps: a cost-effectiveness analysis.

BACKGROUND : For large sessile colorectal polyps (LSCPs), endoscopic mucosal resection without diathermy ("cold endoscopic mucosal resection [EMR]") is gaining popularity because of its safety advantages over conventional EMR ("hot EMR"). Polyp recurrence rates have been reported to be higher with cold EMR. Considering these differences, we performed a cost-effectiveness analysis of these two techniques. METHODS : A decision analysis model was constructed for EMR of an LSCP. The decision tree incorporated the EMR method, clip use, procedural mortality, adverse events and their management, and polyp recurrence. Outcomes included days of lost productivity and marginal cost difference. Adverse event and recurrence rates were extracted from the existing literature, giving emphasis to recent systematic reviews and randomized controlled trials. RESULTS : Through 30 months of follow-up, the average cost of removing an LSCP by cold EMR was US$5213, as compared to $6168 by hot EMR, yielding a $955 cost difference (95 % confidence interval $903-$1006). Average days of lost productivity were 6.2 days for cold EMR and 6.3 days for hot EMR. This cost advantage remained over several analyses accounting for variations in recurrence rates and clip closure strategies. Clip cost and LSCP recurrence rate had the greatest and the least impacts on the marginal cost difference, respectively. CONCLUSION : Cold EMR is the dominant strategy over hot EMR, with lower cost and fewer days of lost productivity. In theory, a complete transition to cold EMR for LSCPs in the USA could result in an annual cost saving approaching US$7 million to Medicare beneficiaries.

Outcomes associated with comorbid diabetes among patients with COPD exacerbation: findings from the ACURE registry

BackgroundDiabetes is a common comorbidity among patients with exacerbation of chronic obstructive pulmonary disease (AECOPD). Diabetes has been reported to be associated with length of stay (LOS), death, and cost among AECOPD patients. However, most studies are retrospective or have small sample sizes. The association for cost has not been researched using diabetes as a main analytic factor. This study aimed to fill gaps mentioned above, to compare basic characteristics between the diabetic and non-diabetic group, and to detect associations between diabetes and clinical outcomes among patients hospitalized with AECOPD.MethodsA total of 5334 AECOPD patients, classified into diabetic and non-diabetic group, were included from a prospective multicenter patient registry study. Generalized linear regression and logistic regression were separately used for the association between diabetes and direct hospitalization cost and the association between diabetes and LOS.ResultsGenerally, diabetic patients had a more severe profile, including being older, more overweight or obese, having more former smokers, more emergency room visits in the past 12 months, and more comorbidities occurrence. Diabetic patients also had worse clinical outcomes, including higher cost and longer LOS. Additionally, the generalized linear regression indicated that the marginal mean cost difference between diabetic and non-diabetic patients was RMB (¥) 775.7.ConclusionsAECOPD patients with comorbid diabetes had a more severe profile and higher direct hospitalization cost. Diabetes screening and integrated care programs might help reduce the heavy comorbidity and economic burden. Moreover, corticosteroids and metformin could be considered in the treatment of these patients.Trial registration Clinicaltrials.gov with the identifier NCT0265752.

Robust Estimation of Marginal Abatement Cost of Water Pollutant: Evidence from Yangtze River Basin

Based on the econometric method of bootstrap for 1000 times, this study estimated the marginal abatement cost of water pollutant, COD and NH3-N, for 9 provinces and 2 municipalities in the Yangtze River Basin from 2001 to 2017 by building a robust estimation model. We found that the marginal abatement cost increases at an average annual rate of 19.47%. The marginal abatement cost in Jiangsu and Sichuan are significantly higher than other regions. Differences in marginal abatement cost make it possible to trade emission rights between regions.

Convex Relaxations of the Short-Term Hydrothermal Scheduling Problem

This paper concerns the assessment of two methods for convex relaxation of the short-term hydrothermal scheduling problem. The problem is originally formulated as a mixed integer programming problem, and then approximated using both Lagrangian and Linear relaxation. The two relaxation methods are quantitatively compared using a realistic data description of the Northern European power system, considering a set of representative days. We find that the Lagrangian relaxation approximates system operational costs in the range 55-81% closer to the mixed integer programming problem solution than the Linear relaxation. We show how these cost gaps vary with season and climatic conditions. Conversely, the differences in both marginal cost of electricity and reserve capacity provided by the Lagrangian and Linear relaxation are muted.